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Question

A small block of mass m is projected horizontally with speed u where friction coefficient between block and plane is given by μ=cx, where x is displacement of the block on plane. Find maximum distance covered by the block
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A
ucg
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B
u2cg
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C
2ucg
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D
u2cg
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Solution

The correct option is A ucg
Because μ=cx
u=u
For mass 'm', N=mg
f=μmg
a=μmgm=μg
Here a= retardation by friction=μg=cgx
Because
a=vdvdx=cgx
ouvdv=cgxoxdx
[v22]ou=cg(x22)xo
u22=cgx22
x=ucg.

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